Abstract:
We present an efficient algorithm to approximate the swept volume (SV) of a complex polyhedron along a given trajectory. Given the
boundary description of the polyhedron and a path specified as a parametric curve, our algorithm enumerates a superset of the boundary surfaces of
SV. It consists of ruled and developable surface primitives, and the SV corresponds to the
outer boundary of their arrangement. We approximate this boundary by using a five-stage pipeline. This includes
computing a bounded-error approximation of each surface primitive, computing unsigned distance fields on a uniform grid, classifying
all grid points using fast marching front propagation, iso-surface reconstruction,
and topological refinement. We also present a novel and fast algorithm for computing the signed distance of surface primitives
as well as a number of techniques based on surface culling, fast marching level-set methods and rasterization hardware to improve the performance
of the overall algorithm. We analyze different sources of error in our approximation algorithm and highlight its performance on complex
models composed of thousands of polygons. In practice, it is able to compute a bounded-error approximation in tens of seconds
for models composed of thousands of polygons sweeping along a complex trajectory.

In each column, from left to right,
each figure shows a generator model, sweeping trajectory, and two views of the
resulting SV approximation reconstructed by our SV algorithm, respectively. In each row, each figure shows different benchmarking model,
from top to bottom, X-Wing, Air Cylinder, Swing Clamps, Hammer, Input Clutch, Pipe, and Pivoting Arms,
respectively.